Facets of Holographic Duality

We now present in more detail the content of this thesis. We refrained from giving an extensive introduction for non experts, either to string theories, or to the AdS/CFT correspondence3 . Rather, we have collected the material resulted from the work done in the last two years in connection to Type 0 string theory, AdS / CFT correspondence, and Holography, expanding it and discussing it in more detail. Moreover we have included some unpublished results that were achieved in the course of research, and which we feel can be a useful complement to the main material. The dissertation is organized as follows: Chapter 1. Very basic facts about strings and branes are recalled. The aim of this chapter is to set the notation and prepare the ground for discussing Type 0 string theories. Chapter 2. Contains a detailed overview of Type 0 string theories. In Section 2.1, we discuss the construction of closed string spectra, stressing their relationships with Type II theories, from the point of view of orbifold constructions. \!Ve illustrate the Type 0 D-branes, and their mapping under orbifold operations. Then we discuss some world-sheet aspects, and their use in computation of effective actions. Finally, in Section 2.4 the possibility of extending Type 0 theories in dimensions different from ten is analyzed, and a concrete proposal for their effective theories is given. Chapter 3. In the first section, by means of simple examples we introduce the idea of applying the AdS/CFT correspondence to Type 0 theories. In Section 3.2 explicit solutions of the Type 0 gravities are provided, for a general range of dimensions. After studying some of their properties, namely ~tability, entropy, and dual Wilson loops, we comment on their dual field theory meaning. Finally, we introduce the subject of holographic flows, to be discussed in much grater details later, by deforming the above Type 0 solutions. Chapter 4. The first section contains an extensive introduction to holographic . flows, with attention to some subtleties that can arise in implementing them. In the next two sections we give two applications of these ideas, illustrating also why the Hamiltonian formalism can be useful in deriving and interpreting the solutions. The first concerns the case of a single scalar field arising from d = 7 N = 1 gauged supergravity. The analysis is complemented with some numerical calculations. The second example touches an independent issue - that of SCFT's dual to compactifications on "non-spherical" manifolds, and holographic flows among them. The section contains also the computation of a two-scalar effective action arising from compactification of M-Theory on the manifold N(l, 1). In Section 4.4 we motivate the use of Hamilton-Jacobi theory for studying flows, and Holography in general. Finally, we comment on holographic anomalies and present a novel way of deriving the holographic Weyl anomaly. Chapter 5. Here we focus on some features of Holography including spin-~ fermions and form fields, in the framework of Hamilton-Jacobi theory. First we motivate our study, also giving an example concerning spinors in the AdS/CFT correspondence. In Section 5.3 we derive, in any dimension and signature, the ADM Hamiltonian for a generic theory of gravity coupled to spin-~ fermions and antisymmetric tensor fields. We then discuss under which conditions the system gives rise to a so-called Callan-Symanzik equation following from the zero-energy constraint. In Section 5.5 we complete the discussion considering the full set of Hamiltonian constraints, regarding them as Ward identities in the dual holographic theory. Some amusing conditions follow from the diffeomorphism constraint. We also present an expansion up to second non trivial order of the on-shell action. Finally the conclusions are given. Appendices. Contain formulae useful in doing Hamiltonian reduction and the complete analysis of fermionic phase-spaces. Both for the complex and the real cases